Continuous dynamical systems that realize discrete optimization on the hypercube

Abstract

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0,1} n . The search is achieved by a gradient-like system in [0,1] n with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0,1} n . Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context.